Application of the Plane-Wave-Based Perturbation Theory to the Density Modulation Induced by a Point Charge in an Electron Gas
The induced electron density at the position of a single point charge Z embedded in a three-dimensional degenerate electron gas is studied at high densities. The perturbative, plane-wave-based treatment developed within the framework of density matrices by March and Murray (Phys Rev 120: 830, 1960, ) is applied here up to second order in Z. Comparison with the result obtained by considering the exact scattering enhancement in a bare Coulomb field is made. The small numerical difference found in the second-order term of the induced density at contact is analyzed following Wigner’s (Phys Rev 94: 77, 1954, ) similar perturbative treatment of the proton field in the hydrogen atom. The impact of the many-body screening is discussed as well.
This note is dedicated to Professor Norman H. March. The authors are indebted to him for many useful, enlightening discussions in the past, and hope that the future will allow further fruitful collaborations. One of us (MLG) acknowledges the financial support of MINECO (Project MTM2014-57129-C2-1-P) and Junta de Castilla y Leon (VA057U16).
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